# Random planar graphs

Universitat Politècnica de Catalunya

Let be a graph chosen uniformly at random among all labelled planar graphs
with vertices. Which are the typical properties of such a random planar
graph?

We show that has about edges, where
is a constant
completely determined, and that deviations from are with high
probability of small order. Among other properties, we also show that is
connected with probability tending to a constant

The basic technique we use in the proofs is singularity analysis of counting
generating functions, considered as complex valued functions.

#### Footnotes

- ... Noy
^{1}
- joint work with Omer Gimenez

2005-05-23